Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T15:59:23.690Z Has data issue: false hasContentIssue false
  • English
  • Français

INDEX NUMBERS AND REVEALED PREFERENCE RANKINGS

Published online by Cambridge University Press:  27 November 2018

Per Hjertstrand ,
James L. Swofford  and
Gerald A. Whitney
Per Hjertstrand
Affiliation:
Research Institute of Industrial Economics
James L. Swofford*
Affiliation:
University of South Alabama
Gerald A. Whitney
Affiliation:
University of New Orleans
*
Address correspondence to: James Swofford, Department of Economics and Finance, University of South Alabama, Mobile, AL 36688, USA; e-mail: [email protected]. Phone: +1 251 460 6705.
Get access Rights & Permissions [Opens in a new window]

Abstract

For previously identified weakly separable blockings of goods and assets, we construct aggregates using four superlative index numbers, the Fisher, Sato-Vartia, Törnqvist, and Walsh, two non-superlative indexes, the Laspeyres and Paasche, and the atheoretical simple summation. We conduct several tests to examine how well each of these aggregates “fit” the data. These tests are how close the aggregates come to solving the revealed preference conditions for weak separability, how often each aggregate gets the direction of change correct, and how well the aggregates mimic the preference ranking from revealed preference tests. We find that, as the number of goods and assets being aggregated increases, the problems with simple summation manifest.

Keywords

Superlative Index NumbersAggregationPreference OrderingsWeak Separability
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 1 , January 2021 , pp. 81 - 99
Copyright
© Cambridge University Press 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank two referees, Bill Barnett, and participants at the Society for Economic Measurement conference in Thessaloniki in July 2016 and the 3rd HenU/Infer Workshop on Applied Macroeconomics in March 2017 in Kaifeng for very helpful comments. Hjertstrand would like to thank the Jan Wallander och Tom Hedelius, Marcus och Marianne Wallenberg, and Johan och Jakob Söderberg foundations for financial support.

References

Afriat, S. N. (1967) The construction of utility functions from expenditure data. International Economic Review 8, 66–77.CrossRefGoogle Scholar
Balk, M. B. (1995) Axiomatic price theory: A survey. International Statistical Review 63, 63–93.CrossRefGoogle Scholar
Barnett, W. A. (1980) Economic monetary aggregate: An application of index number and aggregation theory. Journal of Econometrics 14, 11–48.CrossRefGoogle Scholar
Barnett, W. A. and Choi, K.-H. (2008) Operational identification of the complete class of superlative index numbers: An application of Galois theory. Journal of Mathematical Economics 44, 603–612.CrossRefGoogle Scholar
Caves, D. W., Christensen, L. R. and Diewert, W. E. (1982) The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica 50, 1393–1414.CrossRefGoogle Scholar
Cherchye, L., Demuynck, T., De Rock, B. and Hjertstrand, P. (2015) Revealed preference tests for weak separability: An integer programming approach. Journal of Econometrics 186, 129–141.CrossRefGoogle Scholar
Chrystal, K. A. and MacDonald, R. (1994) Empirical evidence on the recent behavior and usefulness of simple-sum and weighted measures of the money stock. Federal Reserve Bank of St. Louis Review 76, 73–109.Google Scholar
Diewert, W. E. (1976) Exact and superlative index numbers. Journal of Econometrics 4, 115–145.CrossRefGoogle Scholar
Diewert, W. E. (1978) Superlative index numbers and consistency in aggregation. Econometrica, 46, 883–900.CrossRefGoogle Scholar
Diewert, W. E. (1993) Overview of volume 1. In: Diewert, W. E. and Nakamura, A. O. (eds.), Essays in Index Number Theory, pp. 1–31. Amsterdam: Elsevier Science Publishers B.V.Google Scholar
Diewert, W. E. and Parkan, C. (1985) Tests for the consistency of consumer data. Journal of Econometrics 30, 127–147.CrossRefGoogle Scholar
Elger, T. and Jones, B. E. (2008) Can rejections of weak separability be attributed to random measurement error in the data? Economic Letters 99, 44–47.CrossRefGoogle Scholar
Fleissig, A. R. and Whitney, G. A. (2003) A new PC-based test for Varian’s weak separability conditions. Journal of Business and Economic Statistics 21, 133–144.CrossRefGoogle Scholar
Fleissig, A. R. and Whitney, G. A. (2008) A nonparametric test of weak separability and consumer preferences. Journal of Econometrics 147, 275–281.CrossRefGoogle Scholar
Fisher, I. (1922) The Making of Index Numbers. Boston, MA: Houghton-Mifflin.Google Scholar
Friedman, M. and Schwartz, A. J. (1963) A Monetary History of the United States, 1867–1960. Study by the National Bureau of Economic Research. Princeton: Princeton University Press.Google Scholar
Friedman, M. and Schwartz, A. J. (1970) Monetary Statistics of the United States: Estimates, Sources, Methods. Study by the National Bureau of Economic Research. New York: Columbia University Press.Google Scholar
Hicks, J. R. (1946) Value and Capital, 2nd ed. Oxford: Clarendon Press.Google Scholar
Hjertstrand, P. (2009) A Monte Carlo study of the necessary and sufficient conditions for weak separability. Advances in Econometrics 24, 151–182.CrossRefGoogle Scholar
Hjertstrand, P., Swofford, J. L. and Whitney, G. (2016) Mixed integer programming revealed preference tests of utility maximization and weak separability of consumption, leisure and money. Journal of Money Credit and Banking 58, 1547–1561.CrossRefGoogle Scholar
ILO (2004) Consumer Price Index Manual: Theory and Practice. Geneva: International Labour Organization. Downloadable at: www.ilo.org/wcmsp5/groups/public/---dgreports/---stat/documents/presentation/wcms_331153.pdf.Google Scholar
IMF (2005) Producer Price Index Manual: Theory and Practice. Washington, D.C.: International Monetary Fund. Downloadable at: https://www.imf.org/external/pubs/ft/ppi/2010/manual/ppi.pdf.Google Scholar
Jones, B. E., Dutkowsky, D. H. and Elger, T. (2005) Sweep programs and optimal monetary aggregation. Journal of Banking & Finance 29, 483–508.CrossRefGoogle Scholar
Leontief, W. V. (1936) Composite commodities and the problem of index numbers. Econometrica 4, 35–59.CrossRefGoogle Scholar
Samuelson, P. A. (1983) Foundations of Economic Analysis, Enlarged Edition. Cambridge, MA: Harvard University Press.Google Scholar
Schrijver, A. (1998) Theory of Linear and Integer Programming. Chichester, England: John Wiley & Sons.Google Scholar
Swofford, J. L. and Whitney, G. A. (1994) A revealed preference test for weakly separable utility maximization with incomplete adjustment. Journal of Econometrics 60, 235–249.CrossRefGoogle Scholar
Varian, H. R. (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110.CrossRefGoogle Scholar
Vartia, Y. (1976) Ideal log-change index numbers. Scandinavian Journal of Statistics 3, 121–126.Google Scholar